Per-Ola Larsson

Control signal constraints and filter order selection for PI and PID controllers

Large control signal derivatives or inter-sample differences may harm actuators. An optimization constraint limiting such variations, related to measurement noise, is derived. Using the constraint, optimal PI, PID and measurement filters with different orders are designed for several processes and compared to the optimal linear controller of high order found via Youla parametrization. Simulations of load disturbance rejections and measurement noise sensitivities are shown and conclusions on filter order selection for PI and PID controllers are drawn.

Comparison Between Robust PID and Predictive PI Controllers with Constrained Control Signal Noise Sensitivity

A performance comparison between PID and predictive PI (PPI) controllers, i.e., two different prediction methods, is presented. Optimization of controller and measurement filter parameters, considering load disturbance rejection, robustness and noise sensitivity, is performed for a batch of industrially representative processes. For a majority of the processes and the constraints chosen, results show that the performances of the controllers are similar. However, the PID controller yields better performance for processes where increased phase and gain may be achieved over a wider frequency interval than what is possible by the PPI controller.

A framework for nonlinear model-predictive control using object-oriented modeling with a case study in power plant start-up

In t his paper, nonlinear model predictive control (NMPC) is applied to the start-up of a combined-cycle power plant. An object-oriented first-principle model library expressed in the high-level language Modelica has been written for the plant and used to set up the simulation and optimization models. The NMPC optimization problems are both encoded, using a high-level notation, and solved in the open-source framework JModelica.org. The results demonstrate the effectiveness of the framework and its high-level description. It bridges the gap between an intuitive physical modeling format and state of the art numerical optimization algorithms. Promising closed-loop control results are shown for plant start-up when the NMPC model contains parametric errors and the simulation model, corresponding to the real plant, is subject to disturbances.

Model-Based Optimization of Economical Grade Changes for the Borealis Borstar Polyethylene Plant

Economical grade changes are considered for a Borealis Borstar polyethylene plant model, incorporating two slurry-phase reactors, one gas-phase reactor and a recycle area with three distillation columns. The model is constructed in the Modelica language and the JModelica.org platform is used for opti- mization. The cost function expresses the economical profit during a grade change and is formulated using on-grade intervals for seven polymer quality variables such as melt index, density and reactor split factors. Additionally, incentives to produce polymer with quality variables on grade target values, not only inside grade intervals, are added. Twelve inflows and three purge flows are used at optimization. Two grade changes are thoroughly reviewed, showing the effect of using a cost function that regards plant economy. Re- sulting trajectories can be divided into three phases with distinguishing fea- tures, and the synchronization of inflows and usage of recycle area off-gas flows are important in the grade changes. (Less)

Cost function design for economically optimal grade changes for a polyethylene gas phase reactor

This paper considers optimization of stationary production and dynamic grade changes for a gas phase polyethylene reactor. The designed cost function considers costs of inflows and revenues from produced polymer. At dynamic optimization, the cost function uses grade variable intervals for defining on-grade polymer and includes economical incentives to produce on-target polymer. Additionally, it also considers a preparatory time interval prior defined transition time, used for economical preparation of reactor state. A previously published model of a gas phase reactor is used and several grade changes are optimized, showing the effects of an economical cost function.

Modeling and Optimization of a Grade Change for Multistage Polyethylene Reactors

Abstract Grade changes in polyethylene reactors, i.e., changes of operating conditions, are performed on a regular basis to adapt to market demands. In this paper, a dynamic optimization procedure is presented built upon the Modelica language extended with Optimica constructs for formulation of optimization problems. A Modelica library for the Borstar® multistage polyethylene reactors at Borealis AB, consisting of two slurry and one gas phase reactor, has been constructed. Using http://JModelica.org , a framework to translate dynamic optimization problems to NLP problems, optimal grade transitions between grades currently used at Borealis AB, can be calculated. Optimal inflows and grade key variables are shown.

Modelica Based Grade Change Optimization for a Polyethylene Reactor

This paper presents a dynamic optimization procedure of grade changes of polyethylene production. The optimization is built upon a novel modular Modelica library containing e.g., non-linear DAE models for polyethylene reactors based on models currently used in nonlinear MPC of industrial reactors at Borealis AB. Using Optimica, which extends the Modelica language with constructs for optimization problems, and JModelica.org, a novel framework to translate such optimization problems into NLP problems, grade transition ptimization problems can be solved. The solution procedure and a transition xample with optimal inputs and outputs are given in the paper showing promising results.

Calibration of a polyethylene plant for grade change optimisations

A polyethylene plant model coded in Modelica and based on a nonlinear MPC model currently used at Borealis AB is considered for calibration. A case study of model calibration at steady-state for four different operating points are analysed, both when looking at one operating point separately, but also to calibrate several simultaneously. Both model parameters and reactor inputs are calibrated for true plant measurement data. To solve the parameter estimation problem, the JModelica.org platform is used, offering tools to express and solve calibration problems. Calibration was obtained with narrow confidence intervals and shows a potential to improve the model accuracy by changing the parameter values. The results will be used for dynamic optimisations of grade changes. *

Relations Between Control Signal Properties and Robustness Measures

In this paper we consider control signal properties, such as maximum magnitude and activity, as well as system robustness measures. We derive an ideal controller and control signal for exponential disturbance rejection for a first order process with time delay. For the resulting closed-loop system, it is shown analytically that there are strong interconnections between robustness measures and control signal properties regarding load disturbance attenuation. The results imply that popular controller design methods implicitly take control signal properties into consideration.